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It can just be reciprocal recommendation rather than being paid, but generally yes, be wary. My mate had the worst situation (shared ownership) where the Housing Association pretty much dictated the solicitor he had to use (unsurprisingly they were shit, even managed to get the address of the property wrong).
Reading some of this stuff makes me realise how good my guy (and the other side) were for my sale/purchase. He always answered the phone and progressed stuff quickly and the other side were swift too (probably helped that I was buying off a developer so definitely a valued client for them).
Staying on topic: if any company - broker / estate agent / bank - recommends a solicitor to you, be very, very suspicious. The will be being paid to make that recommendation.